Finite Group DatabasebetaFinite Group Databasebeta| order | 1792 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C7 · Schur multiplier (H2) = C22×C4 |
| direct product | #127×AGL(1,𝔽8) |
| unambiguous semidirect product | (C23×#127)⋊C7 |
| Fitting, Sylow | C23×#127 ⋊ C7 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C23×AGL(1,𝔽8) |
| commutator, socle, cosocle | C25 | C23×C7 |
| Fitting | C23×#127 | C7 |
| hypercenter | #127 | AGL(1,𝔽8) |
| hypocenter | C23 | C7×#127 |
| LCS | G ▷ C25 ▷ C23 | |
| UCS | C1 ◁ C22 ◁ #127 | |
1917 conjugacy classes of subgroups; only the 78 normal subgroups are shown.
This group has 1917 conjugacy classes of subgroups — too many to draw. Only its 78 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 112 |
112 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1792, 1083525);